The motivation of thread/state correspondence originated from finding an effective scheme to characterize the entanglement structure between different bulk extremal surfaces in the framework of SS duality, or explicitly constructing the dual states (hereinafter referred to as SS states) of these extremal surfaces. This is inspired by the following two notable simple rules in the SS duality [1]}, [2]}, [3]}: \(\bf rule ~1:\)  the density matrix corresponding to an extremal surface is a direct product of the density matrices at each point. In other words, a bulk extremal surface corresponds to an equal-probability mixed state; \(\bf rule ~2:\)  a closed surface corresponds to a pure state. Due to rule 1, one can imagine that on an extremal surface associated with an entropy \(S\)  (i.e., with an area of \(4{G_N}S\) ), there distribute exactly \(S\)  bits (each with only two basic states, \(\left| 1 \right\rangle \)  and \(\left| 0 \right\rangle \) ). Then, for any bulk extremal surface \(\gamma \)  with an entropy \({S_\gamma }\) , we can label its basic states as \(\left\lbrace  {\left| {\gamma = q} \right\rangle \left| {q \in N,0 \le q \le {2^{{S_\gamma }}} - 1} \right.} \right\rbrace \) . Each decimal number \(q\)  exactly corresponds to a binary string that describes the overall configuration state of all the SS bits on \(\gamma \) . The SS state corresponding to \(\gamma \)  can be represented as a mixed state \({\rho _\gamma }\)  equipped with equal probabilities [3]}:
\({\rho _\gamma } = \sum \limits _{q = 0}^{{2^{{S_\gamma }}} - 1} {\frac{1}{{{2^{{S_\gamma }}}}}\left| {\gamma = q} \right\rangle \left\langle {\gamma = q} \right|} .\) 
